A Connecticut teenager at the center of a 16-month custody battle involving the Massachusetts child protection agency was allowed to spend Father’s Day at home without any state supervision, a sign that her parents may be on the brink of getting full custody of her.

“She came home, and we did a barbecue,” Lou Pelletier, her father, said in a telephone interview Sunday night from the family’s West Hartford home.

Pelletier said his wife, Linda, who has been staying at a hotel near Justina’s residential treatment center in Thompson, Conn., drove the 16-year-old to the family home early Sunday afternoon. Justina then went with family members to a Cirque du Soleil show, followed by a dinner barbecue at the house with her parents and her three sisters.

The teen’s father said this was Justina’s second visit to the house without any supervision. The first visit, he said, took place about two weeks ago and lasted about two hours. His wife, on her own, has also been allowed to drive Justina to at least one visit at Tufts Medical Center, he said.

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“She’s got pretty much freedom now,” the father said, referring to Justina.

For most of the time Justina has been in state custody, her parents have been restricted to supervised visits at agency locations once a week.

Lou Pelletier said his Father’s Day was much happier with Justina home for the day, but he said he was angry that she had to leave after dinner. His wife drove their daughter back to the JRI Susan Wayne Center for Excellence in Thompson, where she has been since last month, he said.

In the custody of the Massachusetts Department of Children and Families since February 2013, Justina spent most of last year at Boston Children’s Hospital, and then about four months this year at a facility in Framingham.

Three months ago, in a sharply worded opinion highly critical of the parents’ conduct, the judge gave permanent custody of Justina to DCF, and said he believed psychological issues explained much of the teenager’s ailments.

However, top officials at DCF earlier this month filed papers with the judge suggesting the parents had made significant progress and recommended that custody return to the parents.

The judge has not set a hearing to decide the case, but he asked all parties to submit paperwork by last Friday, and he could also rule any time without a hearing.

On Sunday, the girl’s father referred to Juvenile Court Judge Joseph Johnston as the “corrupt judge” who has yet to authorize Justina’s release back to her parents’ custody. He also said that when Justina is finally returned to the family, “there is going to be a firestorm” of legal action against the state of Massachusetts for taking custody in the first place.

When asked about Justina’s current physical condition, he said she is eating adequately, but her bowels still do not work normally and she still relies on a tube placed in her intestines that enables her system to be “flushed” periodically each day.

He said she still cannot walk, and family members must to lift her out of the car and bring her into the house. She continues to rely on a wheelchair.

Justina’s custody dispute began in early 2013 when her mother brought her to Children’s Hospital, saying her daughter was suffering from severe symptoms of mitochondrial disorder, a rare metabolic disorder. She said her daughter was not eating, her speech was slurred, and she had trouble walking.

Within a few days, however, Children’s disputed this diagnosis, saying that Justina’s problems were primarily psychological, and her parents were blocking psychiatric care that she badly needed.

The hospital staff filed medical child abuse charges with DCF, and the agency then took emergency custody of Justina when the parents threatened to discharge her.

The father said Sunday night that he is confident that Justina suffers from mitochondrial disorder, and that the idea that she has major psychological issues is a “scam.”

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